Was Joshua assumed into heaven in Zechariah chapter 3?

No. Zechariah 3 is a courtroom vision about the cleansing and restoration of Jerusalem, not an assumption. The Joshua standing there is Joshua the high priest of the return from exile, not Joshua the son of Nun from the book of Joshua. No, he was not. And let me clear up the confusion that probably produced the question, because it is a reasonable one. There are two different men named Joshua. The Joshua of Zechariah 3 is Joshua the high priest, the man who led worship at the rebuilding of the Temple after the Babylonian captivity. He is not Joshua the son of Nun, who led Israel into Canaan roughly a thousand years earlier. The confusion is made worse by the Douay, which renders the name in its Greek and Latin form: "And the Lord showed me Jesus the high priest standing before the angel of the Lord." That is the same name. Joshua, Jeshua, Jesus: one Hebrew name coming to us through Greek. It is the high priest of the restoration who is standing there in filthy garments, not the conqueror of Jericho. Now, what the vision actually is. It is a courtroom scene, and it is one of the clearest pictures of Satan's function in the Old Testament that we have. Joshua stands before the angel of the Lord, "and Satan stood on his right hand to be his adversary. And the Lord said to Satan: The Lord rebuke you, O Satan, is not this a brand plucked out of the fire?" Satan is doing precisely what his name means and what Job 1:6 to 12 and Apocalypse 12:10 describe: he is the accuser of the brethren. He is contesting the Lord's mercy, and he has material to work with, because Jerusalem's sins were many and real. The Lord does not deny the sins. He overrules the accusation. The brand plucked out of the fire is Jerusalem itself, saved not because she deserved it but because God chose to save her. St. Jude uses the same image when he tells us to save others by snatching them out of the fire (Jude 1:23). So the filthy garments are taken off Joshua and clean ones put on him. That is a cleansing and a restoration to priestly office, with a promise about the Branch who is to come. It is not a translation to heaven. There is not a word in the chapter about Joshua being taken up, and his whole significance in the vision depends on his remaining where he is, at the head of the restored priesthood in Jerusalem. For comparison, consider a passage that genuinely does involve an assumption and an argument with Satan: Jude 9, on the body of Moses. Scripture says the Lord buried Moses (Deuteronomy 34:6), and yet Moses appears bodily on the Mount of the Transfiguration some fifteen hundred years later, which tells us that sometime after the burial the Lord raised him and assumed his body. Satan very likely disputed it, on the argument that Moses had been barred from Canaan for not trusting God (Numbers 20:12; Deuteronomy 34:1 to 5), and Michael would not bring a railing accusation against him but said only, "The Lord command you." Notice that Zechariah 3 is cited right alongside Jude 9 precisely because both show Satan in the accuser's role, not because both show an assumption. That parallel in role is probably what made someone read an assumption into Zechariah 3. It is not there. The short list of those who were assumed bodily into heaven is Enoch, Elijah, Moses, Our Lady, and possibly the people raised at the crucifixion in Matthew 27:53. The rest of the Old Testament saints are in heaven in their disembodied souls, awaiting the resurrection of their bodies on the last day, when soul and body will be reunited (John 5:28 to 29; 6:39 to 40; 1 Corinthians 15:42 to 50). Joshua the high priest is among them, and so is Joshua the son of Nun. Neither is an exception, and Scripture nowhere says otherwise.